Reyes, who played for five seasons at for his boyhood club before moving to Arsenal in 2003, struck 15 minutes from time to salvage a point for Atletico from a match they should have won.
It was the second time that Quique Sanchez Flores's side had to come from behind. Alvaro Negredo had given the visitors the lead at the end of a half the home side had dominated, only for Koke to level soon after the restart.
However, a point apiece does little for either side. Sevilla remain in seventh place while Atletico move up one spot to eighth, above Real Sociedad on goal difference.
Atletico were dominant from the outside as the pressure on coach Flores continued to grow pre-kick-off.
They spurned countless chances, with Sergio Aguero the main culprit, although reserve goalkeeper Javi Varas made some important saves.
Atletico were level right after the break when midfielder Koke headed in Diego Forlan's cross for his first ever goal for Atletico.
Midway through the half Sevilla went ahead again when Rakitic guided home Jesus Navas's cross, after Atletico had again been enjoying the bulk of the possession.
Aguero missed several more opportunities to draw level before the Argentine clipped a long ball on for Reyes to latch on to and finish calmly for his fourth goal of the season.
Espanyol have 40 points from 25 matches, two ahead of Bilbao, who host third-placed Valencia on Sunday. Sevilla have 35 in seventh and Atletico are on 34 in eighth.